in-25-30-perform-the-indicated-operations-and-write-the-result-in-simplest-form-in-each-case-list--6

Question

In $25-30,$ perform the indicated operations and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined.
$$
\frac{x^{2}-3 x+2}{4 x} \cdot \frac{12 x^{2}}{x^{2}-2 x} \div \frac{x-1}{x}
$$

Alisa Lu · Accepted Answer

So for this question, were given a series of fractions were asked to perform a series of operations on them. I&#x27;m just going to look at the 1st 2 so I&#x27;m going to factor out the numerator here. To be X minus two or times X minus. Waas over for X is being multiplied by a 12 x square and factory out of X here. That will give us X minus two. So from here, we can say that our X value cannot be equal to zero or two, as that would make these denominators equal to zero. So now we can cancel her before here before here, making this three in this actual cancel with one of these X is making this three X. Now, we can say that this X will cancel with this ex just getting rid of the ex entirely. This X minus to cancel this X minus two. And now we&#x27;re left with three times X minus one over one. So this will give us an answer of three times X minus one over one. Now it&#x27;s asking us to the by this answer by X minus one over X, which is the same as multiplying by. There was cyclical of X minus one over X. So you could say that this is equal to three X minus one over one times X over X minus one. So here, in this fraction, ex cannot be zero, and we&#x27;ve already put a limit. Their butt X can also not be equal to one as that, with this denominator equal to zero. So we have to write. X cannot be even one as well. So now we can say that this X minus one cancels with this X minus one. And so we&#x27;re just left with three acts over one, which is just three X s O. That is our answer.

Alisa Lu · Answer

So for this question, were given a polling a mule divided by a fraction times fraction. So I&#x27;m just gonna look at the pollen well divided by a fraction. First of so, the polynomial were given its X squared minus two X close one, and this is being divided by X minus one over three. Dividing by fraction is the same as multiplying by. It&#x27;s reciprocal. You can say that. X squared minus two X close. One is being multiplied by three over X minus one. So the numerator over here will factor out into X minus one times X minus one over one times three X minus one. So over here, it&#x27;s important to note that our ex cannot equal positive one, as that would make our denominator here equal to zero. So these X minus ones cancel out and we&#x27;re just left with three times X minus one over one. And now we have to multiply this by X plus four over three X. So now we have to say that our ex can also not be equal to zero, as that would make this denominator equal to zero. So the three here cancels out with this three and now we&#x27;re just left with X minus one times X plus four over X and so that is our final.

Alisa Lu · Answer

So for this question, when given like a string of different operations that we need to perform. So I&#x27;m going to look at the first half right now, which is three x over X minus one times X squared, minus one over X. So let&#x27;s go ahead and constrain our X value. So ex cannot be cool one or zero as thieves would make the denominator equal to zero. So before I multiply across and go to factor out the numerator here and this gives me three x over X minus one times X minus, one times x plus one over X and then I&#x27;m going to do some cancellation. This X minus one cancels with this X minus one and this X cancels with this ex leaving us with just three x plus one under one. Now we need to divide this by X plus one over three. Dividing by X plus one over three is the same as multiplying by the reciprocal of X plus one over three. So we can say that three X plus three times X plus one is being multiplied by three over X plus one. And so here we have to say that our ex cannot equal negative one as that would make our solution. Uh, I mean, our denominators here. So these X plus ones cancel out and we&#x27;re just slept with three times three over one, which is equal to nine. So that&#x27;s your final answer.

Alisa Lu · Answer

So for this question, they&#x27;re asking us to subtract. Um What? Well, they&#x27;re asking us to do subtraction on this fraction to x squared, plus one over five X minus seven X square minus one over by Lex. And so we have to say that ex cannot be equal to zero, as that would make the denominator evil to zero. So now, from here, we can just go ahead and some tracked because you already have a common denominator to x squared minus seven x Where gives you negative five x squared and then one minus and negative one is same s one plus one. So that&#x27;s just too. And all of this is over five mics.

Georgiann Andersen · Answer

Okay, We&#x27;re gonna simplify. Simplify the following expression. This is number 20. The expression is one over X plus one over X minus two. Subtract two over X squared minus two X. Okay, First thing we&#x27;re gonna do is simplify the third term. You&#x27;re gonna simplify the third turn. So two over x x squared me this two X, it&#x27;s gonna be too over X times X minus two. Then we&#x27;re gonna combine second term with the third term. So we&#x27;re gonna take one over X minus two and we&#x27;re gonna subtract two x times X minus two. Which is gonna be We need to take X times about the numerator and denominator. The first fractions. So it&#x27;s gonna be a over X minus two. Tracked the two over X X minus two and we&#x27;re gonna end up with X minus two O R X times X minus two. We can cancel the X minus twos out, leaving us with one over X. Now we can come fine. The first term with this one. So one over. EPS, it&#x27;s one over X. It&#x27;s gonna be too over x to make this an undefined statement. Ex cannot be zero or two

Derrick Hanson · Answer

So while the beginning of this problem is multiplication, I do see that later on I have some division. First thing I want to do then is take care of that and change that to multiplication by flipping or finding the reciprocal of the fraction. Right? Remember the fraction? The second fraction meeting? The fraction that comes after the division sign is the one that we find the reciprocal of that we flip meeting. I&#x27;m gonna rewrite to a over A plus two. I&#x27;m simply going to rewrite a squared minus 4/4 A squared because that last fraction a minus two over a Because that fraction comes after the division sign. In order to change this division to multiplication, we will have to flip that fraction or find the reciprocal of it meeting. Now it will be a over a minus two. Now that I have everything being multiplied on this problem, I can start going through and factoring out each of my individual pieces of possible and then see what I can simplify. See what I can reduce. See what I can cancel to a is already factored. Nothing special there. A plus two is a quantity so it also is factored because there&#x27;s nothing in common that we could pull out of there, a squared minus four that can be factored because their two terms they&#x27;re a squared and four. There is subtraction between them, and they both can square perfectly, meaning this is a difference of squares if you remember the way difference of squares works. Since there&#x27;s two terms, they both squared perfectly, and there&#x27;s a difference between them and subtraction. The way we factor it is, I need to ask myself, What is the square root of a squared? All the square root of a squared is a and then I ask myself, What&#x27;s the square root of four square to four is, too, so both of my quantities are going to be a end to. One of them will simply be plus, and one of them will be minus on. The bottom four can be split into two times two. A squared can be split into a times A on the last fraction. A is just a nothing special there, and a minus two is a quantity, so it doesn&#x27;t have anything to cancel area that doesn&#x27;t have anything to pull out of it to factor out. Everything has split up here. Let&#x27;s see how we can cancel. Remember, you have to have the same thing between the numerator and the denominator top and bottom. In order for it to cancel. For example, I see we have a two and my numerator and we have a two in my denominator, So skin canceled. I see I haven&#x27;t a in my numerator and I haven&#x27;t a In my denominator, those can cancel. I see. I have a quantity of a plus two in my numerator and a quantity of a plus two In my denominator, those can cancel. I see. I have a quantity of a minus two in my numerator and a quantity of a minus two. In my denominator, those can cancel. I see. I have a quantity earned. I just have a standalone A in my numerator and I have a standalone A in my denominator. Those king cancel a lot of stuff canceled here, which is a great mix, at least to me. It makes me feel like we actually did this problem for a reason, because we&#x27;re getting a much simpler answer, right? Looks like everything in my numerator has canceled. So remember that would leave us with a one, not zero, but a one. We&#x27;re multiplying here, So everything&#x27;s cancelled. 21 Looks like almost everything cancels in my denominator. Except for this too. So our answer for this problem would be 1/2. All we have to do now is figure out what values of a would cause this equation to be undefined. Remember, that means we have to include every single denominator, both pre and post finding the reciprocal. Now, these two denominators right here were the same in both cases. So we don&#x27;t have to do those twice. We just do them once. But my third fraction I have to solve out for when the denominator was a and I have to solve out after we flipped it for when the denominator was a minus two. We have to do both. Meaning there are four parts here. Four denominators that we have to solve out. So we have a plus two is not allowed to equal zero. Remember, we&#x27;re saying not equal to zero because if you get zero in the Dominator, that&#x27;s what gives you undefined. All right, we&#x27;re saying zero is what we don&#x27;t want. So that&#x27;s why we&#x27;re playing slash to the equal sign. We&#x27;ve got four. A squared does not equal zero. We have a does not equal zero. And finally we have a minus two does not equal zero. We just need to solve all of these out for the 1st 1 Subtract two over and you would get that A cannot equal negative too. For this one, you divide by four and get a squared does not equal zero. The opposite of squaring is square rooting so you would square root. But you just end up with a does not equal zero which is the same thing as what we already had here. So we don&#x27;t have to repeat them. Finally add to over and you would get that a does not equal positive too. So our final answer is 1/2 as long as a does not equal negative too a does not equal zero and a does not equal positive too

Problem 30 Hard Difficulty

In $25-30,$ perform the indicated operations and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined.
$$
\frac{x^{2}-3 x+2}{4 x} \cdot \frac{12 x^{2}}{x^{2}-2 x} \div \frac{x-1}{x}
$$

Answer

$3 x ; x \neq 0,2$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

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Absolute Value - Example 1

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$3 x ; x \neq 0,2$

Algebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Heather Z.

Kayleah T.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Heather Z.

Kayleah T.

Ann Xavier Gantert

Algebra 2 and Trigonometry